Appropriate Pixel Size for Orthophotography
Hans-Peter Bähr
Institute for Photogrammetry and Remote Sensing, University of Karlsruhe
Englerstrasse 7, D-7500 Karlsruhe 1, Germany
Email: bähr@ipf.bau-verm.uni-karlsruhe.de
Things are going to change drastieally by digital
image processing. This is beeause 3D-information
of the Earth's surfaee is stored in large data
bases, no matter what data acquisition system
was applied: The data bases provide eompatibility.
Images will generally be a very important layer in
Geo-Information Systems. Moreover, images are the
starting point for automatie data extraction. All these
factors eontribute to the fact, that digital orthophotos
suddenly are beeoming more and more important for
industry and application (COLOMINA et al. 1991,
HÖHLE 1992, MAYR 1992).
Abstract
Pixel size is a basic parameter for digital imagery.
It is shown, that there exists no general rule for
an appropriate pixel size: It is a function of many
parameters, like object frequency, image quality,
specific application andeconomical restrictions of date
processing and storage.
Zusammenfassung
Pixelgröße ist ein Basisparameter für digitale Bilder.
Es wird gezeigt, daß keine allgemeinen Regeln
für geeignete Pixelgrößen existieren: Sie ist eine
Funktion vieler Parameter, wie Objektfrequenz,
Bildqualität, jeweilige Anwendung und wirtschaftliche Beschränkungen von Bildverarbeitung und speicherung.
1
2
Economical Considerations
for Orthophoto Production
Reeent presentation of digital orthophoto systems by
industry show that production costs apparently have
dropped to economy level. This is really prooved
by BÄHR/WIESEL 1991, giving approx. US $ 25
computing eost for colour orthophotos of 230 mm
x 230 mm standard format plus manpower. The
equation
Introduction
(1)
presents the total cost C of an orthophoto as a
function of instrument Gi and instrument time ti
plus man power cost Gm and operator time t m .
Though today the man power component is still higher
than the instrument component, there is a chance
that manpower costs will drop considerably when
automation is more commonly applied.
Orthophotos, i. e. rectified photogrammetric imagery,
are used sinee many deeades as a substitute
or a supplement for topographie maps. There
exist without doubt many advantages like quiek
and eeonomie production, actual and eomplete
information, espeeially for the environmental domain.
Considering pixel size of digital orthophotos, it of
course enters ti in equation (l). Therefore, i twill
always be an important factor, even if instrument cost
will continue to go down.
Nevertheless, orthophotography was not always
generally aceepted like one should have expected
(e. g. KELLERSMANN 1985). This was due to
eompletely different technology from eonventional
eartography: a half-tone paper-print photography
is not "compatible" to a eonventional line map.
Combinations of both products are offered ("photo
maps")and show the way to follow in future:
This is a particular factor for digital systems which
does not exist for analog systems, where "geometrie
resolution" principally does not play an important
role for economy, exept for scale considerations, which
finally are the same for digital systems.
64
For economical consideration we may approximate
the pixel number in a standard photogrammetric
image by
n [MB] '" (0,5· LP)2,
Lp/mm
where LP stands for geometrie resolution in
linepairs/mm (see BÄHR 1989). This relation is
visualised in Fig. 1. Standard values are given by 25
LP /mm and corresponding pixel size of 20 p,m. This
quantity may be exactly stored on a 9-track tape of 6
250 bpi.
SO
Storage will not represent .. a considerable cost factor
any more as shown by BAHR/WIESEL 1991, even
when producing colour orthophotos. Resampling is
a more important factor, infiuencing not only cost
but also time, because the operation al environment,
time for orthophoto production is most important;
"economy" is highly correlated with "time". Adding
the working steps to produce an orthophoto digitally,
reduction of pixel size from 50 to 25 .. p,m raises the
total processing time by 100 % (BAHR/WIESEL
1991).
für
10
100
200
300
Pixel
(MB)
Fig. 1 Data quantity in [MB] as a function of
resolution and pixel size for photogrammetric imagery
(BÄHR 1989)
Therefore, adequate pixel size for orthophotography
has to be selected earefully according to the respeetive
needs in order to meet eost and time requirements.
3
Pixel size [jJm]
3.1
Theoretical considerations
Pixel size is a parameter of image quality, more
specifically a parameter of geometrie resolution,
whieh is always conneeted to (teehnieal or biologieal)
systems. The "real world" has no "resolution", it
ean be represented by a fractional model, whieh IS
teehnieally infinite.
Onee the "real world" is imaged, the imaging proeess
is band limited. This means, that in the frequeney
domain the resulting image H (u, v) is restricted to a
spectral band ±v:
Size
The term "orthophoto" relates to a weH-known analog
reetifieation teehnology, whieh is at its end sinee
digital systems have beeome operational. Data type
is the eonventional, analog photogrammetric image of
230 mm x 230 mm format.
-v
~
H(u, v)
~
+v
(2)
due to Modulation Transfer whieh in praetise always
produces degradation of the image.
H(u, v) = F(u, v). G(u, v)
The word "orthophotography" defines geometrie
properties different from the original central
projection of analog photography. An "orthophoto"
is a standard product in Photogrammetry, somewhat
"historie" on photographie paper.
(3)
where F (u, v) is the spectrum of an original image,
and G (u, v) the transformation funetion.
The Modulation Transfer Function
MTF = IG(u, v)1 in (3), which designes the geometrie
resolution of the system output, is eomposed by the
respective MTF's of the subsystems. For eonventional
orthophotos we may write for instance:
A "digital" orthophoto on the other hand, may be
taken as a standard product, too. This is eorreet,
when it means only the substitution of analog
photographie teehnology by digital eomponents. In
this ease, the final product is weB defined, i. e.
identieal to the eonventional product "on a sheet of
paper" .
MTF
= MTFa
(4)
. MT Fgl MT Fe! MT Fed
However this is for sure not the eorrect way to handle
new ted~nology. Real new teehnology - and digital
image processing in photogrammetry is one - will
neeessarily lead to new products and provoke new
applications, starting may be from the old ones. In the
next paragraphs we shall diseuss the appropriate pixel
size in the light of ehanging technology and ehanging
products.
·MTFol MTFo! MTFod
where the indexes stand for "atmosphere" (a), "lens"
(I) "film" (f)and "development proeess" (d). 1, fand d
appear for both the photogrammetrie eamera (e) and
the orthophoto projector (0); the respective fadors
are not the same (i. e. MTFeJ t= M,TFoJ).
65
Asking for the appropriate pixel size for the image
H (u, v) in (3), it is theoretically given by the
NYQUIST frequency v, i. e. the highest frequency
transferred by the MTF of the whole imaging process
(4). This leads to the well-known Sampling Theorem
a<
-
..!...
2//
3.2
PracticaI considerations
In practise, there is always band limitation as images
in any case have passed a technical or physiological
system in order to be real. Consequently, we may
derive a MTF according to (4); different methods to
do this are reported in BÄHR, 1988.
(5)
giving the descrete pixel values a as a function of the
limiting frequency (supposing isotropie character).
Fig. 2 explains how to derive the appropriate pixel
size from the MTF. After the Sampling Theorem it
corresponds to N /2, where N marks the intersection
of the MTF with the Resolving Threshold of the
Application system (RETAS).
The determination of v, being the basic parameter
for pixel size, is not trivial. J ust one number to
characterize the highly complex data set of a twodimensional image will only present a very rough
referenee. This becomes evident, when analysing
a straight lines in an image. Lines are the most
critical components in (digital) images in theory and
in practise, and therefore we will take them for
discussing some basic issues.
The two curves separate four areas, which caracteristically show the conditions for pixel size:
Only in area 1 the information transported by
theMTF satisfies the requirement of the RETAS;
the areas 2 and 4, below the RETAS curve are
principally excluded, i. e. there exist uo pixel size
which would correspond to the requirement of the
application expressed by the RETAS curve.
An "ideal straight line" theoretically contains all
frequencies, as it is composed of points without space
in between. This may be visualised clearly in the
frequency domain, where straight lines in the image
appear again as straight lines. Consequently, there is
no band limitation for such an "ideal straight line" ,
and any pixel size would deteriorate H.
Area 3 may be varied as a function ofpixel size, which
directly designs the MTF.
It is very important to point out, that two
factors contribute to the appropriate pixel
size, the MTF and the RETAS. As far as the
MTF is concerned, it relates to the input data,
whereas the RETAS relates to the output data.
A straight line is a "model from analytical geometry",
which means a high level of abstraction. By the way,
we run into the same problems for "points", which
again are nothing than an abstract model and do not
exist in reality. In practise, lines do not correspond
rigerously to the ideal model, neither in the real world
nor in the "recorded version" on imagery. One should
add "fortunately", because otherwise there would be
no solution for our question.
Having in mind digital orthophoto production, input
data may for instance be
* Conventional photogrammetric imagery
* Photography from amateur camera
* Scanner imagery from aerial or space platforrns
While scanner imagery is already digital, photography
has to be converted into pixels. This process has to
take into account not only the MTF of the original
photography, but also the RETAS as shown. In other
words, the pixel size has to consider the intended
further application for the output data, which may
for instance be
* Produdion of conventional orthophotos, substituting only analog projection by digital resampling
* Orthophoto layer in digital data base
* Digital orthophotos for separate applications,
like
environmental monitoring or point measurement
o
~------
__________- L___________
N
We take the first point for an example: The final
result, a paper print orthophoto, has to serve for
analysis by a human operator without using visual
assistance by lenses etc. The resolution of the human
eye affords a pixel size of about 50 ftm for 1,4' viewing
angle, given by the theoretical physiological treshold.
This relates to a quality which had been guaranteed
by the conventional rastering and printing process
(see WIESEL, 1985).
LP/mm
Fig. 2: Pix~l size N/2 as a function of MTF
and Resolving Threshold of Application System
(RETAS). For the numbers see text.
66
Evidently, the RETAS of this example does not
seem to be in accordance with the potential of a
photogrammetric image - "its curve in Fig. 2 is too
steep" .
The human eye is not the adequate sensor for looking
at an original photogrammetric image. This of course
does change when armed by a lens, i. e. when
the hatched area in Fig. 2 grows due to smoother
inclination of RETAS.
Conditions for pixel size change considerably when
the human eye is eliminated from the system. This
happens for computer vision, where the input for the
grey values after resampling is a digital system. In
this case, the signal is practically transformed without
any degradation caused by a MTF, and the RETAS
does not exist. Consequently, the digital system may
use the input data fuHy, without regarding a RETAS.
An example is digital correlation of targets (point
signals) as shown by BÄHR (1988), where correlation
accuracy only depends on the number of pixels which
do show gradient effects. This is exclusively a function
of scale.
3a
4
Variable Pixel Size in one
Scene: The degressive Sampling Approach
It is evident, that image scale, geometric resolution
or pixel size should be an issue of the respective
application. Different from analog photography,
digital orthophotography is not necessarily restricted
to a uniform resolution in one scene. Within one scene
we may vary pixel size due to well-defined demands
by operator's request. A very simple example follows
from the above mentioned determination of targets in
computers vision systems: Here small pixels must be
available only in areas elose to the targets. We should
remember that the human vision system depicts
carefully only a very small portion of the sphere by
mecanically moving head and eyeballs and optically
focusing the point of interest.
3b
The selection of different pixel size within one scene
may follow various algorithms, 2 of them have been
studied here. It is one of the advantages ofdigital
image processing, that the processes are controlled
by software and not by hardware.
The objective of the following analysis is to visualise
the effect from variable pixel size in one scene of a
digital orthophoto. The data was scanned from aerial
photography of 1 : 6 000 scale at 50 pm, showing
the Campus of Karlsruhe University, Germany. Fig. 3
gives the original data for three charaderistic objects:
"Cars" (3 a, a parking area and its environment),
"building" (3 b, appartment houses) and "forest" (3 c,
i. e. part of the gardens elose to the famous Karlsruhe
3c
Fig. 3 Test objects from aerial photography 1 : 6 000
50 pm pixel size, area 256 x 256, original (100 %)
a: "cars"j b: "building"; c: "forest"
67
4a
5a
4b
5b
4c
5c
Fig. 4 Effect by uniform data reduction
2 x 2 patches (25 %)
Fig. 5 Effect by uniform data reductioll
4 x 4 patches (6,25 %)
68
6 al
6 a2
6 bl
6 b2
6el
6 c2
Fig. 6 Effect by degressive sampling threshold qlO
a
28,4 %, b
15,7 %, C
18,5 %
=
=
=
69
7 al
7 a2
7 bl
7 b2
7cl
7 c2
Fig. 7 Effect by degressive sampling threshold q20
a = 5,9 %, b = 2,8 %, c = 0,7 %
70
Castle). The smaH scenes include 512 x 512 pixels
each.
Table 1 displays the values obtained for the three
scenes, giving r q and rd as weH as different values
for t a .
In Fig. 4 and 5 the original data have been compressed
to patches of 2 x 2 and 4 x 4, conserving 25 %
and 6,25 % of the original data, respectively. This
uniform approach does not take into account the
image content; consequently it shows a general lowpass filtering effect, which very often will not be
accepted for orthophotos.
For analysing the results, we have 3 references: the
images, the respective pixel pattern (Fig. 6 and 7,
fight column) and table 1. The visualisation shows
that reduction to approx. 20 % of the original pixel
size does not lead to considerable degradation. This is
not the case when using the uniform reduction (Fig.
4 and 5). Moreover, further reduction to below 10 %
is critical as expected. On the other hand, the pixel
Different pixel sizes in one scene lead to considerably
better results as shown in Fig. 6. The algorithmus
used refer to grey value differences. Different grey
values of one patch i are substituted by a single one
(e. g. the me an value) if
pattern show that frequencies of high contrast are
still preserved, even for only 1 % of the original pixel
quantity. The pixel pattern are very useful for the
analysis, as the human eye alone is often mislead.
(6)
where t a is an arbitrary threshold (in greyvalue units)
and ri the result of an algorithm applied to the patch
i.
Very interesting is the process for the forest scene;
here the meadow in the center is substituted by
an isolated single pixel al ready for 18,5 % of the
information. At this stage (t q = 10); high frequencies
of the trees are still preserved. This goes drastically
20 (only 0,7 % of the original
down for t q
information), where no useful information is any more
present.
The procedure may start taking the whole scene
of 256 by 256 grey values as the first patch. The
subsequent patches then are reduced systematicaHy,
following a quadtree approach, going from 4 (of 128 x
128 pixels) to finally 16384 (of 2 x 2 pixels). However
we have to substract from this number those patches,
which have already been assigned to uniform pixels.
A simple approach for
ri
=
Fig. 8 demonstrates clearly the different effect for the
3 scenes. High frequencies afford large pixel numbers,
and "forest" behaves differently from "man made
features" like cars and buildings.
would be
We call the procedure "degressive sampling", for
it starts at smaH pixel sizes and leads to coarser
representation for aeras of lower frequency which in
general may be less interesting. Anyway the potential
of this approach does not end here. Both thresholds
t a and algorithms ri may be varied in order to design
the required result properly.
(7)
n
where n is the pixel number in one patch; j controls
the sum of the individual pixels in that patch and k
their difference from the mean value.
Pixel Number
Instead of the grey value differences their quadratic
sum may be taken, too. This leads to the algorithm r q ,
used for the displayed examples in the figures 6 and
7. The reason for taking r q instead of r d is because
of better contrast for printing. This is a consequence
from the quadratic term.
%
so
40
30
20
Quadr. Difference q Linear Difference p
Cars
Pixel number
%
Building
Pixel number
%
Forest
Pixel number
%
Original
t a = 10
t a = 20
t a = 40
t a = 80
65536
100
18592
28,4
3868
5,9
12313
18,8
2998
4,6
10
4 x 4
atches = 6 25%
20
65536
100
10309
15,7
1867
2,8
8101
12,4
1720
2,6
65536
100
12145
18,5
436
0,7
7372
11,2
709
1,1
40
60
80
Threshold d
Fig. 8 Reduction of pixel numbers in % as a function
of density differences (threshold d) and uniform pixel
clustering (2 x 2 and 4 x 4 patches)
Table 1: Pixel quantity in a 256 x 256 scene for
different scenes algorithms and thresholds
71
5
Conclusion
LITERATURE
BÄHR, H.-P.: Measures for Geometrie Resolution
of Digital Cameras. ISPRS Congress Kyoto, 1988,
CommI
Pixel size will always play an important role for
orthophoto production, even if some parameters, like
data storage, are going to become obsolete. In future,
pixel size is not necessarily any more a fixed standard
value, but within a scene a flexible function of many
parameters, which depend on specific applications.
The degressive sampling approach seems to be a
flexible procedure which consequently makes use
of the potential of digital image processing for
orthophoto production, not accepting uniform pixel
size for a complete scene. The data reduction effect
and the conservation of high frequencies may only
be the starting point for a new thinking. The
next step will apply itfor image segmentation, as a
preprocessing approach.
6
BÄHR, H.-P.: Das digitale Orthophoto und seine
Möglichkeiten. Photogrammetric Week, Stuttgart
1989
BÄHR, H.P.and WIESEL, J.: Cost-Benefit Analysis
of Digital Orthophotos Technology. In: EBNER/FRITSCH/HEIPKE (Eds.) Digital Photogrammetric
Systems, Wichmann Verlag Karlsruhe 1991
WIESEL, J.: Herstellung digitaler Orthophotos.
In: Digitale Bildverarbeitung, Karlsruhe 1985
FA UST, H.-W.: Digitalisierung photogrammetrischer
Bilder.
Zeitschrift für Photogrammetrie und Fernerkundung,
1/1990 S. 6 - 11
HÖHLE, J.: Herstellung von digitalen Orthophotos an einer Arbeitsstation des Geoinformationssystems TIGRIS. Zeitschrift für Photogrammetrie
und Fernerkundung S. 42 - 48, 1992
Acknowledgement
KELLERSMANN, H.: Farbige Luftbildkarten
1 : 5000 - nein, danke? Erfahrungen über den Verkauf
von DrucksWcken. Zeitschrift für Photogrammetrie
und Fernerkundung, S. 19 - 22, 1985
The author gratefully thanks Yuval Fisher/San Diego
for providing the computer programs for degressive
sampling and Heiko J acobs for performing the image
processing.
MAYR, W.: Das photogrammetrisehe Bildverarbeitungssystem von Carl Zeiss. Zeitschrift für
Photogrammetrie und Fernerkundung S. 13 - 18, 1992
COLOMINA, 1.; NAVARRO, J. and TORRE,
M.: Digital Photogrammetric Systems at the I.
C. C. In: EBNER/FRITSCH/HEIPKE (Eds.):
Digital Photogrammetric Systems. Wichmann Verlag
Karlsruhe 1991
72